Inter-mobile body carrier phase positioning device and method

ABSTRACT

The inter-mobile body carrier phase positioning device according to the invention includes: a first observation data acquisition means that acquires observation data concerning a phase accumulation value observed in a first mobile body; a second observation data acquisition means that acquires observation data concerning a phase accumulation value observed in a second mobile body; a satellite pair determination means that determines pairs of satellites used for carrier phase positioning; and a carrier phase positioning means that takes, between each of the pairs of the satellites determined by the satellite pair determination means, a single or double difference between the observation data acquired by the first observation data acquisition means and the observation data ac quired by the second observation data acquisition means, and determines relative positional relation between the first mobile body and the second mobile body by carrier phase positioning using the single or double difference of the observation data.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention relates to an inter-mobile body carrier phase positioningdevice and method in which relative positional relation between mobilebodies is determined.

2. Description of the Related Art

A device for calculating relative position with the use of inter-vehiclecommunication has already been available, the device including arelative position calculating means using a difference in GPS signalpropagation time, which deter nines a difference between data on GPSsignal propagation time with respect to a nearby vehicle and data on GPSsignal propagation time with respect to a host vehicle, and solvessimultaneous equations in the three or more values of the differences inthe GPS signal propagation time thus determined and the relativeposition, which is the unknown, to obtain the relative position of thenearby vehicle with respect to the host vehicle (see Japanese PatentApplication Publication No. 10-148665 (JP-A-10-148665), for example).

In the technology described in JP-A-10-148665, for the purpose ofpositioning, geometrical equations are formulated that are expressedusing the difference in GPS signal propagation time and the directioncosines of the angles formed between axes of the relative coordinatesystem and the line segment between the host vehicle and a satellite,and the equations are simultaneously solved to obtain the relativeposition. In such a configuration, however, there is a problem with thepositioning accuracy because of the fact that only the GPS signalpropagation time with large error is used as the observation data, thefact that the directional cosines of the angles formed between axes ofthe relative coordinate system and the line segment between the hostvehicle and a satellite cannot be accurately determined, etc.

SUMMARY OF THE INVENTION

The invention provides an inter-mobile body carrier phase positioningdevice and method that realize highly accurate positioning.

A first aspect of the invention relates to an inter-mobile body carrierphase positioning device, which includes: a first observation dataacquisition means that acquires observation data that is observed in afirst mobile body and concerns a phase accumulation value of a carrierwave of a satellite signal; a second observation data acquisition meansthat acquires observation data that is observed in a second mobile bodyand concerns a phase accumulation value of the carrier wave of thesatellite signal; a satellite pair determination means that determinespairs of satellites used for carrier phase positioning; and a carrierphase positioning means that takes, between each of the pairs of thesatellites determined by the satellite pair determination means, asingle difference or a double difference between the observation dataacquired by the first observation data acquisition means and theobservation data acquired by the second observation data acquisitionmeans, and determines relative positional relation between the firstmobile body and the second mobile body by carrier phase positioning withthe use of the single difference or the double difference of theobservation data.

In the inter-mobile body carrier phase positioning device of the firstaspect, the observation data acquired by the first observation dataacquisition means and the observation data acquired by the secondobservation data acquisition means may both include determination dataon phase accumulation values of the carrier waves of common satellitesand determination data on pseudoranges of the common satellites; and therelative positional relation is determined by an instantaneouspositioning method in which the observation data are used independentlyfor each epoch.

In the inter-mobile body carrier phase positioning device of the firstaspect, an influence of the single difference or the double differenceof the observation data, taken for each of the pairs, on positioningresult may be regulated by weights, based on a difference betweenreciprocals of distances between the first mobile body and the pair ofthe satellites for each of the pairs of the satellites determined by thesatellite pair determination means.

In the inter-mobile body carrier phase positioning device of the firstaspect, the carrier phase positioning means may determine the relativepositional relation with the use of position information of the firstmobile body obtained by point positioning along with the singledifference or the double difference of the observation data, and theposition information of the first mobile body obtained by the pointpositioning may be obtained by the point positioning using only thesatellites included in the pairs determined by the satellite pairdetermination means.

In the inter-mobile body carrier phase positioning device of the firstaspect, the satellite pair determination means may determine the pairsof the satellites based on the distance between the first mobile bodyand each of the satellites.

In the inter-mobile body carrier phase positioning device of the firstaspect, the satellite pair determination means may pair two satellitessuch that a difference between distances from the first mobile body tothe two satellites is relatively small.

In the inter-mobile body carrier phase positioning device of the firstaspect, the satellite pair determination means may pair two satellitessuch that a difference between reciprocals of distances from the firstmobile body to the two satellites is relatively small.

In the inter-mobile body carrier phase positioning device of the firstaspect, the satellite pair determination means may preferentially selectthe satellite, from which a distance to the first mobile body isrelatively large, to incorporate into the pairs.

In the inter-mobile body carrier phase positioning device of the firstaspect, when a difference between reciprocals of distances from thefirst mobile body to a pair of the satellites exceeds a predeterminedthreshold value, the satellite pair determination means may replace thepair of the satellites by another pair of the satellites.

In the inter-mobile body carrier phase positioning device of the firstaspect, when an integer solution derived in the carrier phasepositioning means is not fixed, the satellite pair determination meansmay preferentially select and use the satellite, from which a distanceto the first mobile body is relatively large, to redetermine the pairs.

The inter-mobile body carrier phase positioning device may be mounted onthe second mobile body, the first observation data acquisition means mayacquire the observation data through radio communication with the firstmobile body, and the second observation data acquisition means mayacquire the observation data through observation of the satellitesignal.

A second aspect of the invention relates to an inter-mobile body carrierphase positioning method, which includes: acquiring first observationdata on a satellite signal observed in a first mobile body; acquiringsecond observation data on a satellite signal observed in a secondmobile body; determining pairs of satellites used for carrier phasepositioning based on distances from the first mobile body to thesatellites so that two of the satellites that are close to each other interms of the distances are paired; and taking, between each of thedetermined pairs of the satellites, a single difference or a doubledifference between the first observation data and the second observationdata, and determining relative positional relation between the firstmobile body and the second mobile body by carrier phase positioning.

BRIEF DESCRIPTION OF THE DRAWINGS

The features, advantages, and technical and industrial significance ofthis invention will be described in the following detailed descriptionof example embodiments of the invention with reference to theaccompanying drawings, in which like numerals denote like elements, andwherein:

FIG. 1 is a system diagram showing an overall system of a globalpositioning system (GPS) to which an inter-mobile body carrier phasepositioning device is applied;

FIG. 2 is a diagram showing main components in a vehicle 20 and avehicle 30;

FIG. 3 is a block diagram showing important processes executed in thevehicles 20 and 30 of an embodiment;

FIG. 4 is a flow chart showing an example of a pair determining processexecuted in an observation data error correction section 40;

FIG. 5 is a flow chart showing a preferable example of the method ofcalculating coordinates on the vehicle 20 side used in inter-vehicle RTKpositioning of the embodiment;

FIG. 6 is a flow chart showing an example of a pair redeterminingprocess executed in the observation data error correction section 40that may be executed after the above-described pair determining processshown in FIG. 4 is executed;

FIG. 7 is a flow chart showing another example of the pair determiningprocess executed in the observation data error correction section 40;

FIG. 8 is a flow chart showing another example of the pair determiningprocess executed in the observation data error correction section 40;and

FIG. 9 is a flow chart showing another example of the pair determiningprocess executed in the observation data error correction section 40.

DETAILED DESCRIPTION OF EMBODIMENTS

An example embodiment for carrying out the invention will be describedbelow with reference to drawings.

FIG. 1 is a system diagram showing an overall system of a globalpositioning system (GPS) to which an inter-mobile body carrier phasepositioning device according to the invention is applied. As shown inFIG. 1, GPS includes GPS satellites 10 that go around the Earth.Vehicles 20 and 30 are on the Earth and can move on the Earth. Note thatthe vehicles 20 and 30 are merely examples of mobile bodies and suchmobile bodies include bicycles, trains, ships, aircrafts, forklifts,robots, information terminals, such as mobile phones, that move withpeople carrying the terminals, etc.

The vehicle 20 is a vehicle that functions as a reference station andhereinafter also referred to as the “reference station.” The vehicle 20however is a mobile reference station unlike the common fixed referencestation.

The vehicle 30 is a subject vehicle of which the position relative tothe vehicle 20 (reference station) is determined, and is a vehicleequipped with the inter-mobile body carrier phase positioning device ofthis embodiment. The vehicle 30, however, may function as the referencestation for another vehicle (vehicle 20, for example) depending on thecircumstances.

The GPS satellites 10 broadcast navigation messages to the Earth at alltimes. The navigation message includes a correction coefficient relatedto the ionosphere, a correction value of the clock, and information onthe orbit of the corresponding GPS satellite 10. The navigation messageis encoded using C/A code and modulated onto L1 carrier wave (frequency:1575.42 MHz), and is broadcast to the Earth at all times.

There are twenty four of GPS satellites 10 going around the Earth at thealtitude of approximately 20,000 km, and four of the GPS satellites 10are evenly arranged in each of six circum-earth orbits that are angledwith respect to each other at angular intervals of 55 degrees. Thus, aslong as the place open to the sky, it is possible to observe at leastfive or more GPS satellites 10 anywhere on the Earth at all times.

FIG. 2 is a diagram showing main components in the vehicle 20 and thevehicle 30. The vehicle 20 is provided with a GPS receiver 22 and aninter-vehicle communications device 24. The vehicle 30 is provided witha GPS receiver 32 and an inter-vehicle communications device 34.

The GPS receivers 22 and 32 each have an oscillator (not shown) thereinof which the frequency is the same as the carrier wave frequency of theGPS satellites 10. The GPS receivers 22 and 32 convert the radio wave(satellite signal), received from the GPS satellites 10 through GPSantennas 22 a and 32 a, into a signal with an intermediate frequency andthen perform C/A code synchronization using the C/A codes generated inthe GPS receivers 22 and 32, thereby extracting the navigation messages.

The GPS receiver 22 determines an accumulation value (D_(ik)(t) of thecarrier wave phase at time t as shown by the following equation, basedon the carrier wave sent from the GPS satellite 10 _(i). The phaseaccumulation value Φ_(ik) may be determined for each of the L1 wave andL2 wave (frequency: 1227.6 MHz).

Φ_(ik)(t)=Θ_(ik)(t)−Θ_(ik)(t−τ _(ik))+N _(ik)+ε_(ik)(t)  (1)

Note that the subscript i (=1, 2, . . . ) of the phase accumulationvalue Φ_(ik) is the number assigned to the GPS satellite 10 _(i), andthe subscript k means that the phase accumulation value Φ_(ik) is theaccumulation value on the reference station side. In addition, N_(ik) isan integer ambiguity and ε_(ik) is a noise (error).

The GPS receiver 22 determines a pseudorange ρ_(ik) based on the C/Acode modulated onto each of the carrier waves sent from the GPSsatellites 10 _(i).

ρ_(ik)(t)=c·τ _(k) +b _(k)  (2)

In this equation, c is light speed and b_(k) is referred to as clockbias, which corresponds to distance error due to the error in the clockin the GPS receiver 22.

The vehicle 20 transmits the phase accumulation value Φ_(ik) and thepseudorange ρ_(ik) determined in the GPS receiver 22 to the vehicle 30through the inter-vehicle communications device 24.

The GPS receiver 32 similarly determines a phase accumulation valueΦ_(iu) of a carrier wave phase based on the carrier waves received fromthe GPS satellites 10 _(i). The phase accumulation value Φ_(iu), may bedetermined for each of the L1 wave and the L2 wave. Note that thesubscript i (=1, 2, . . . ) of the phase accumulation value Φ_(iu) isthe number assigned to the GPS satellite 10 _(i), and the subscript umeans that the phase accumulation value Φ_(iu) is the accumulation valueon the vehicle 30 side. Similarly, the phase accumulation value Φ_(iu)is obtained as the difference between a phase Θ_(iu)(t) of theoscillator at carrier wave reception time t and the carrier wave phaseΘ_(iu)(t−τ) at the time of generation of the satellite signal in the GPSsatellite 10 _(i).

Φ_(iu)(t)=Θ_(iu)(t)−Θ_(iu)(t−τ _(u))+N _(iu)+ε_(iu)(t)  (3)

In this equation, τ_(u) is the time of travel from the GPS satellite 10to the GPS receiver 32 and ε_(iu) is a noise (error). Note that at thetime the observation of the phase difference is started, although theGPS receiver 32 can accurately determine the phase within a cycle of thecarrier wave, the GPS receiver 32 cannot identify the cycle number.Thus, as shown in the above equation, an integer ambiguity N_(iu), whichis the ambiguity term, is included in the phase accumulation valueΦ_(iu)(t).

The GPS receiver 32 determines a pseudorange ρ_(in) based on the C/Acode modulated onto each of the carrier waves sent from the GPSsatellites 10 _(i). The pseudorange ρ_(h), determined in the GPSreceiver 32 includes the error, such as the distance error, as shown inthe following equation.

ρ_(iu)(t)=c·τ _(u) +b _(u)  (4)

In this equation, b_(u) is referred to as clock bias, which correspondsto distance error due to the error in the clock in the GPS receiver 32.

In addition to the determination as described above, the GPS receiver 32performs various processes described below with reference to FIG. 3.

The inter-vehicle communications devices 24 and 34 are designed tointeractively communicate with each other. In this embodiment, theinter-vehicle communications device 24 of the vehicle 20 that functionsas the reference station transmits the phase accumulation value Φ_(ik)and the pseudorange ρ_(ik) that are determined in the GPS receiver 22,to the inter-vehicle communications device 34 of the vehicle 30 througha radio communication network. In the following description, the data onthe phase accumulation value Φ_(ik) and the pseudorange ρ_(ik) that aredetermined in the GPS receiver 22 is also collectively referred to asthe “observation data,” the data on the phase accumulation value ρ_(ik)is also referred to as the “L1 data” and the “L2 data,” corresponding tothe L1 wave and the L2 wave, respectively, and the data on thepseudorange ρ_(ik) is also referred to as the “C/A data”.

FIG. 3 is a block diagram showing important processes executed in thevehicles 20 and 30 of this embodiment. Note that, concerning theconfiguration in the vehicle 30, while sections 42, 44, 46, and 48 areimplemented by the GPS receiver 32 in this embodiment, these sectionsmay be implemented by another microcomputer or the like connected to theGPS receiver 32.

As shown in FIG. 3, in the vehicle 20 that functions as the referencestation, data to be transmitted, which is the observation data includingthe L1 data, L2 data, and C/A data that are observed, is generated everypredetermined period of time and supplied to the vehicle 30. In thevehicle 20, the position of the vehicle 20 is determined everypredetermined period of time and the determined position is supplied tothe vehicle 30. The positioning may be realized by point positioningusing the observed C/A data, for example. The point positioning methodusing C/A data is widely available and the description thereof isomitted.

The vehicle 30 receives the observation data from the reference stationside every predetermined period of time. The GPS receiver 32 acquiresthe phase accumulation value Φ_(iu) (L1 data and L2 data) and thepseudorange ρ_(iu) (C/A data) on the vehicle 30 side. The observationdata on the reference station side and the observation data on thevehicle 30 side may be synchronized using GPS time, a pulse-per-second(PSS) signal, or the like. The observation data on the reference stationside and the observation data on the vehicle 30 side are first suppliedto an observation data error correction section 40.

In the observation data error correction section 40, the error in theobservation data is eliminated by appropriately pairing the observationdata on the reference station side and the observation data on thevehicle 30 side. The specific process executed in the observation dataerror correction section 40 will be described later. In the observationdata error correction section 40, basically, a plurality of pairs of theGPS satellites 10 that are used in the inter-vehicle real time kinematic(RTK) positioning are selected from the plurality of satellites 10 thatcan be observed by both the reference station and the vehicle 30, insuch a manner that principal error components Δ of the inter-vehicle RTKpositioning are minimized. Specifically, a plurality of pairs of the GPSsatellites 10, between each of which the double difference of theobservation data is taken, are determined so that the principal errorcomponents Δ of the inter-vehicle RTK positioning are minimized. Thenumber of pairs of the GPS satellites 10 that are determined is four ormore, which is required for positioning.

Each of the principal error components Δ of the inter-vehicle RTKpositioning is expressed by the following equation.

Δ_(jh)=ε(1/D _(jk)−1/D _(hk))

In the above equation, D_(jk) is the distance between the vehicle 20 andthe GPS satellite 10 _(j) and calculated based on the result ofpositioning of the vehicle 20 (result of the above-mentioned pointpositioning, for example) and the position of the GPS satellite 10 _(j).The position of the GPS satellite 10 _(j) may be calculated using thesatellite orbit information contained in the navigation message, and/orthe calendar data provided by an organization, such as the internationalGPS service (IGS). Similarly, D_(hk) is the distance between the vehicle20 and the GPS satellite 10 _(h) and calculated based on the result ofpositioning of the vehicle 20 (result of the above-mentioned pointpositioning, for example) and the position of the GPS satellite 10 _(h).The meaning of the error components A that are expressed by theequation, Δ_(jh)=ε(1/D_(jk)−1/D_(hk)), will be described later.

The weight adjustment section 42 determines the weighting coefficients w(weight components of a matrix) used in the real solution calculatingsection 44 described later, and adjusts the weight for each pair of theGPS satellites 10. Basically, in the weight adjustment section 42, inorder that the result of positioning is not significantly affected, alower weight is assigned to a pair with a larger error component Δdescribed later, as compared to a pair with a smaller error component Δ.

In the real solution calculating section 44, the position of the vehicle30 (typically, the relative position with respect to the vehicle 20) isdetermined by the least square method, in which the observed amount isthe double difference of the observation data and state variables arethe position of the vehicle 30 and the double difference of the integerambiguity. For example, the position of the vehicle 30 may be determinedin the procedure described below. Although, in the description below,for the sake of simplicity, a case is described where the phaseaccumulation value of the L1 wave only is used, when the phaseaccumulation value of the L2 wave is also used, the phase accumulationvalue of the L2 wave may be additionally dealt with similarly to thecase of the phase accumulation value of the L1 wave.

The double difference of the phase accumulation values of the two GPSsatellites 10 _(j) and 10 _(h) (i=j, h, j≠h) that are paired isexpressed by the following equation.

Φ^(jh) _(ku)=(Φ_(jk)(t)−Φ_(ju)(t))−(Φ_(hk)(t)−Φ_(hu)(t))  (5)

Meanwhile, because of the physical meaning, (distance between GPSsatellite 10 _(i) and GPS receiver 22 or 32)=(wave length L of carrierwave)×(phase accumulation value), the double difference Φ^(jh) _(ku), ofthe phase accumulation value is expressed as follows.

$\begin{matrix}{\Phi_{ku}^{jh} = \frac{\begin{bmatrix}{\begin{Bmatrix}{\sqrt{\begin{matrix}{\left( {{X_{k}(t)} - {X_{j}(t)}} \right)^{2} + \left( {{Y_{k}(t)} - {Y_{j}(t)}} \right)^{2} +} \\\left( {{Z_{k}(t)} - {Z_{j}(t)}} \right)^{2}\end{matrix}} -} \\\sqrt{\begin{matrix}{\left( {{X_{u}(t)} - {X_{j}(t)}} \right)^{2} + \left( {{Y_{u}(t)} - {Y_{j}(t)}} \right)^{2} +} \\\left( {{Z_{u}(t)} - {Z_{j}(t)}} \right)^{2}\end{matrix}}\end{Bmatrix} -} \\\begin{Bmatrix}{\sqrt{\begin{matrix}{\left( {{X_{k}(t)} - {X_{h}(t)}} \right)^{2} + \left( {{Y_{k}(t)} - {Y_{h}(t)}} \right)^{2} +} \\\left( {{Z_{k}(t)} - {Z_{h}(t)}} \right)^{2}\end{matrix}} -} \\\sqrt{\begin{matrix}{\left( {{X_{u}(t)} - {X_{h}(t)}} \right)^{2} + \left( {{Y_{u}(t)} - {Y_{h}(t)}} \right)^{2} +} \\\left( {{Z_{u}(t)} - {Z_{h}(t)}} \right)^{2}\end{matrix}}\end{Bmatrix}\end{bmatrix}}{L + N_{ku}^{jh} + ɛ_{ku}^{jh}}} & (6)\end{matrix}$

In this equation (6), (X_(k)(t), Y_(k)(t), Z_(k)(t)) are coordinates ofthe reference station 20 in the world coordinate system at time t,(X_(j)(t), Y_(u)(t), Z_(u)(t)) are coordinates (unknown) of the vehicle30 at time t, and (X_(j)(t), Y_(j)(t), Z_(j)(t)) and (X_(h)(t),Y_(h)(t), Z_(h)(t)) are coordinates of the GPS satellites 10 _(j) and 10_(h) at time t, respectively. N^(jh) _(ku) is the double difference ofthe integer ambiguity, that is, N^(jh)_(ku)=(N_(jk)−N_(ju))−(N_(hk)−N_(hu)). Note that time t is synchronizedbased on the GPS time, for example.

The double difference of the pseudoranges with respect to the two GPSsatellites 10 _(j) and 10 _(h) (i=j, h, j≠h) at time t is expressed bythe following equation.

ρ^(jh) _(ku)=(ρ_(jk)(t)−ρ_(ju)(t))−(ρ_(hk)(t)−ρ_(hu)(t))  (7)

The double difference ρ^(jh) _(ku) of the pseudorange is expressed asfollows.

$\begin{matrix}{\rho_{ku}^{jh} = {\begin{Bmatrix}{\sqrt{\left( {{X_{k}(t)} - {X_{j}(t)}} \right)^{2} + \left( {{Y_{k}(t)} - {Y_{j}(t)}} \right)^{2} + \left( {{Z_{k}(t)} - {Z_{j}(t)}} \right)^{2}} -} \\\sqrt{\left( {{X_{u}(t)} - {X_{j}(t)}} \right)^{2} + \left( {{Y_{u}(t)} - {Y_{j}(t)}} \right)^{2} + \left( {{Z_{u}(t)} - {Z_{j}(t)}} \right)^{2}}\end{Bmatrix} - \begin{Bmatrix}{\sqrt{\left( {{X_{k}(t)} - {X_{h}(t)}} \right)^{2} + \left( {{Y_{k}(t)} - {Y_{h}(t)}} \right)^{2} + \left( {{Z_{k}(t)} - {Z_{h}(t)}} \right)^{2}} -} \\\sqrt{\left( {{X_{u}(t)} - {X_{h}(t)}} \right)^{2} + \left( {{Y_{u}(t)} - {Y_{h}(t)}} \right)^{2} + \left( {{Z_{u}(t)} - {Z_{h}(t)}} \right)^{2}}\end{Bmatrix}}} & (8)\end{matrix}$

(X_(k)(t), Y_(k)(t), Z_(k)(t)), (X_(u)(t), Y_(u)(t), Z_(u)(t)),(X_(j)(t), Y_(j)(t)), and (X_(h)(t), Y_(h)(t), Z_(h)(t)) in the equation(8) are the same as those of the above equation (6). Note that time t issynchronized based on the GPS time, for example.

The relation between an observed amount Z and a state variable isexpressed by the following linear model.

Z=H·η+V  (9)

In this equation, V is an observation noise. η represents statevariables, which are coordinates (unknown) of the vehicle 30 and thedouble difference of the integer ambiguity. For example, η=[X_(u),Y_(u), Z_(u), N¹² _(ku), N¹³ _(ku), N¹⁴ _(ku), N¹⁵ _(ku)]^(T)(superscript T means transpose) when the pairs (j, h) of the GPSsatellites 10 are four pairs (1, 2), (1, 3), (1, 4), and (1, 5). Theobserved amount Z in the equation (9) is the double difference Φ^(jh)_(ku) of the phase accumulation value (see the above equation (5)) andthe double difference ρ^(jh) _(ku) of the pseudorange (see the aboveequation (7)). For example, Z=[Φ¹² _(ku), Φ¹³ _(ku), Φ¹⁴ _(ku), Φ¹⁵_(ku), ρ¹² _(ku), ρ¹³ _(ku), ρ¹⁴ _(ku), ρ¹⁵ _(ku)]^(T) when the pairs(j, h) of the GPS satellites 10 are four pairs (1, 2), (1, 3), (1, 4),and (1, 5). Although the observation equation (9) is linear, theobserved amount Z is non-linear with respect to the state variablesX_(u), Y_(u), and Z_(u) in the equations (6) and (8), and therefore,each of the terms in the equations (6) and (8) is partiallydifferentiated with respect to the state variables X_(u), Y_(u), andZ_(u), whereby the observation matrix H of the above equation (9) isobtained. For example, when the pairs (j, h) of the GPS satellites 10are four pairs (1, 2), (1, 3), (1, 4), and (1, 5), the observationmatrix H is as follows.

H₁ in the equation (10) is an observation matrix when the observedamount Z₁ is expressed as Z₁=[Φ¹² _(ku), Φ¹³ _(ku), Φ¹⁴ _(ku), Φ¹⁵_(ku)]^(T) and H₂ in the equation (10) is an observation matrix when theobserved amount Z₂ is expressed as Z₂=[ρ¹² _(ku), ρ¹³ _(ku), ρ¹⁴ _(ku),ρ¹⁵ _(ku)]^(T), so that the observation matrix H includes the twoobservation matrices H₁ and H₂.

When the above equation (9) is solved by least square method using theobservation matrix H of the equation (10), the real solution (floatsolution) of η can be obtained as follows.

η=(H ^(T) ·W·H)⁻¹ ·H ^(T) ·W·Z  (11)

W is a weight matrix of which the weights are adjusted in the weightadjustment section 42, and for example, when the pairs (j, h) of the GPSsatellites 10 are four pairs (1, 2), (1, 3), (1, 4), and (1, 5), theweight matrix W is as follows.

$\begin{matrix}{W = \begin{pmatrix}w_{1} & \; & \; & \; & \; & \; & \; & \; \\\; & w_{2} & \; & \; & \; & \; & \; & \; \\\; & \; & w_{3} & \; & \; & 0 & \; & \; \\\; & \; & \; & w_{4} & \; & \; & \; & \; \\\; & \; & \; & \; & w_{\rho 1} & \; & \; & \; \\\; & \; & \; & \; & \; & w_{\rho 2} & \; & \; \\\; & {0\;} & \; & \; & \; & \; & w_{\rho 3} & \; \\\; & \; & \; & \; & \; & \; & \; & w_{\rho 4}\end{pmatrix}} & (12)\end{matrix}$

The diagonal elements w₁, w₂, w₃, and w₄ are weighting coefficientsrelated to the observed amount Z₁ and the diagonal elements w_(ρ1),w_(ρ2), w_(ρ3), and w_(ρ4) are weighting coefficients related to theobserved amount Z₂. These coefficients may be determined using theprincipal error components Δ_(jh) of the inter-vehicle RTIC positioning.For the pair (1, 2) of the GPS satellites 10 as a representativeexample, w₁ may be expressed as w₁=|1/Δ₁₂|, and in this case, w_(ρ1) maybe expressed, using a coefficient γ (γ is between 1/200 and 1/100, forexample), as w_(ρ1)=γ|1/Δ₁₂|. Alternatively, for the pair (1, 2) of theGPS satellites 10 as a representative example, w₁ may be expressed asw₁=(1/Δ₁₂)², and in this case, w_(ρ1) may be expressed, using acoefficient γ (γ is between 1/200 and 1/100, for example), asw_(ρ1)=γ(1/Δ₁₂)². In consideration of the fact that the C/A data islower in accuracy than L1 data (or L2 data), w_(ρ1) is set less than w₁by using the coefficient γ less than 1.

In the integer solution calculating section 46, an integer solution ofthe integer ambiguity is calculated based on the real solution (floatsolution) of the integer ambiguity calculated in the real solutioncalculating section 44. For example, an integer solution (wave number)with the minimum error with respect to the real solution calculated inthe real solution calculating section 44 is determined as the firstcandidate, and an integer solution with the next minimum error isdetermined as the second candidate. As a method of performing thisprocess, the LAMBDA method may be used in which decorrelation of theinteger ambiguity is performed to reduce the size of the integer searchspace, and then the solution is determined. Alternatively, instead ofthe LAMBDA method, another integer least square method or simplerounding off may be used to derive the integer solution.

In the FIX determination section 48, it is determined whether theinteger solution derived in the integer solution calculating section 46is employed as the solution. Specifically, the reliability of theinteger solution derived in the integer solution calculating section 46is determined, and when an integer solution with high reliability isobtained, the integer solution is fixed and thereafter, the RTKpositioning using this integer solution is performed to output theresult of positioning. There are various methods of determining thereliability of an integer solution, and any appropriate method may beused. For example, the reliability of an integer solution may bedetermined using a ratio test. For the purpose of explaining an exampleof the ratio test, it is assumed that the pairs (j, h) of the GPSsatellites 10 are four pairs (1, 2), (1, 3), (1, 4), and (1, 5), andfour real solutions (n¹², n¹³, n¹⁴, n¹⁵) of the integer ambiguities,first) candidates (N¹² ₁, N¹³ ₁, N¹⁴ ₁, N¹⁵ ₁) and second candidates(N¹² ₂, N¹³ ₂, N¹⁴ ₂, N¹⁵ ₂) of the integer ambiguities are calculated.In this case, as shown below, the ratio R is the ratio of a first normto a second norm, the first norm being the norm between the realsolutions of the integer ambiguities and the second candidates of theinteger solutions of the integer ambiguities, the second norm being thenorm between the real solutions of the integer ambiguities and the firstcandidates of the integer solutions of the integer ambiguities.

R={(n ¹² −N ¹² ₂)²+(n ¹³ −N ¹³ ₂)²+(n ¹⁴ −N ¹⁴ ₂)²+(n ¹⁵ −N ¹⁵ ₂)²}/{(n¹² −N ¹² ₁)²+(n ¹³ −N ¹³ ₁)²+(n ¹⁴ −N ¹⁴ ₁)²+(n ¹⁵ −N ¹⁵ ₁)²}  (13)

In general, the higher the value of the ratio R is, the higher thereliability of the first candidates of the integer solutions of theinteger ambiguities is. Thus, an appropriate predetermined thresholdvalue α may be set, and when the ratio R is higher than thepredetermined threshold value α, it may be determined that thereliability of the integer solution is high and the first candidates ofthe integer solutions of the integer ambiguities may be accepted.

Next, the process of determining pairs executed in the observation dataerror correction section 40 will be described.

FIG. 4 is a flow chart showing an example of the pair determiningprocess executed in the observation data error correction section 40.

In step 400, the distance D_(ik) between the vehicle 20 and the GPSsatellite 10 ₁ is calculated based on the result of positioning of thevehicle 20 supplied from the vehicle 20 (reference station). In thisstep, the GPS satellites 10 ₁, for each of which the distance D_(ik) iscalculated, may be all of the common GPS satellites 10 that are beingobserved by both the vehicle 20 and the vehicle 30. The positions of theGPS satellites 10 ₁ may be calculated using the satellite orbitinformation contained in the navigation message and/or the calendar dataprovided by an organization, such as the international GPS service(IGS).

In step 402, two GPS satellites 10 ₁ that are close to each other interms of the distance D_(ik) are paired based on the distances D_(ik)with respect to the GPS satellites 10 ₁ obtained in step 400. Thus, itis possible to determine the pairs such that the principal errorcomponents Δ_(jh) (=ε(1/D_(jk)−1/D_(hk))) of the inter-vehicle RTKpositioning are small. As a result, the accuracy of the result ofpositioning performed using the thus determined pairs becomes high. Notethat the number of pairs determined in step 402 only has to be greaterthan the number of pairs that is required for the positioningcalculation. For example, the number may be four (fixed value) orotherwise, the number may be equal to or greater than four and variable.In the latter case, the number may be varied depending on the degree ofcloseness between the distances D_(ik), for example.

The principal error components Δ (=ε(1/D_(ik)-1/D_(hk))) of theinter-vehicle RTK positioning are obtained by expanding the equations(6) and (8) around the coordinates (X_(k), Y_(k), Z_(k)) of the vehicle20 and extracting the principal, point positioning error components.Specifically, in the case of the equation (6), for example, when X_(k)is taken and the equation (6) is partially differentiated with respectto X_(k), the following equation is obtained.

$\begin{matrix}{\frac{\partial\Phi_{ku}^{jh}}{\partial X_{k}} = {{{- \frac{1}{L}}\frac{X_{j} - X_{k}}{\sqrt{\left( {X_{j} - X_{k}} \right)^{2} + \left( {Y_{j} - Y_{k}} \right)^{2} + \left( {Z_{j} - Z_{k}} \right)^{2}}}} + {\frac{1}{L}\frac{X_{h} - X_{k}}{\sqrt{\left( {X_{h} - X_{k}} \right)^{2} + \left( {Y_{h} - Y_{k}} \right)^{2} + \left( {Z_{h} - Z_{k}} \right)^{2}}}}}} & (14)\end{matrix}$

Because the point positioning error is sufficiently smaller than thevalue of the denominator (actual distance between the vehicle 20 and theGPS satellite 10 _(i)), when the root portions of the denominator areexpressed by the distances D_(jk) and D_(hk) calculated using the pointpositioning result and the left side of the equation (14) is representedby A, the equation (14) is expressed as follows.

$\begin{matrix}{A = {{\frac{1}{L}\frac{X_{h} - X_{k}}{D_{hk}}} - {\frac{1}{L}\frac{X_{j} - X_{k}}{D_{jk}}}}} & (15)\end{matrix}$

Meanwhile, with regard to the numerator, when the point positioningerror in the X_(k) direction is ε, that is, when X_(k) obtained by pointpositioning is expressed, using the true value X_(kr), by the equationX_(kr)=X_(k)+ε, the equation (15) is expressed by the followingequation, whereby the point positioning error componentΔ_(jh)(=ε(1/D_(ik)−1/D_(hk))) is extracted.

Note that while X_(k) only is taken in the above description, Δ_(jh) inthe similar form (different only in ε) are extracted also with respectto Y_(k) and Z_(k).

Thus, according to the process shown in FIG. 4, two of the GPSsatellites 10 _(i) are paired that are close to each other in terms ofthe distance D_(a), and the inter-vehicle RTK positioning is performedusing the pairs of the GPS satellites 10 _(i), so that it is possible toavoid the problem characteristic of the inter-vehicle RTK positioning,that is, the deterioration in the positioning accuracy caused by usingthe coordinates that are obtained by point positioning (accuracy is inthe order of one meter) instead of the coordinates that are accuratelydetermined as the coordinates on the reference station side (accuracy isin the order of one millimeter). Specifically, according to the processshown in FIG. 4, two of the GPS satellites 10 _(i) are paired that areclose to each other in terms of the distance D_(ik), and theinter-vehicle RTK positioning is performed using the pairs of the GPSsatellites 10 _(i), so that, even when the coordinates on the referencestation side are determined by a positioning method with low accuracy,such as point positioning, it is possible to minimize the influence ofsuch a positioning method and realize highly accurate positioning.

Next, a preferable example of the method of calculating coordinates onthe vehicle 20 (reference station) side will be described with referenceto FIG. 5.

FIG. 5 is a flow chart showing a preferable example of the method ofcalculating coordinates on the vehicle 20 side used in the inter-vehicleRTK positioning of this embodiment. The process shown in FIG. 5 isexecuted in the GPS receiver 22 on the vehicle 20 side.

In step 500, the information for identifying the pairs of the GPSsatellites 10 _(i) used in the RTK positioning on the vehicle 30 side isacquired from the vehicle 30 through communication between theinter-vehicle communications devices 24, 34. Specifically, the GPSreceiver 22 acquires the information for identifying the pairs of theGPS satellites 10 _(i) determined by the above-described process shownin FIG. 4.

In step 502, the position of the vehicle 20 is determined by pointpositioning with the use of, the GPS satellites 10 _(i) alone that areincluded in the pairs of the GPS satellites 10 _(i) used in the RTKpositioning. For example, if the pairs (j, h) of the GPS satellites 10_(i) used in the RTK positioning on the vehicle 30 side are four pairs(1, 2), (1, 3), (1, 4), and (1, 5), even when another GPS satellite 10_(i) (GFS satellite 10 ₆, for example) can be observed by the vehicle30, the C/A data of the five GPS satellites 10 ₁, 10 ₂, 10 ₃, 10 ₄, and10 ₅ are used to determine the position of the vehicle 20 by pointpositioning.

In step 504, the result of point positioning (coordinates of theposition of the vehicle 20) obtained in the above step 502 istransmitted, along with the observation data, to the vehicle 30 throughcommunication between the inter-vehicle communications devices 24, 34.

In this way, according to the process shown in FIG. 5, the position ofthe vehicle 20 is determined by point positioning with the use of theGPS satellites 10 _(i) alone that are included in the pairs of the GPSsatellites 10 _(i) used in the RTK positioning on the vehicle 30 side,and therefore, when the RTK positioning is performed on the vehicle 30side with the use of this positioning result, the influence of the pointpositioning error present in the position of the vehicle 20 isefficiently reduced, and it is therefore possible to realize highlyaccurate positioning.

Note that the process shown in FIG. 5 may be executed in the GPSreceiver 32 on the vehicle 30 side. This is because the GPS receiver 32on the vehicle 30 side receives the observation data (C/A data) from theGPS receiver 22 and therefore, it is possible to determine the positionof the vehicle 20 by point positioning also by using the GPS receiver 32on the vehicle 30 side. With this configuration, it is possible toreduce the amount of communication between the vehicle 20 and thevehicle 30.

FIG. 6 is a flow chart showing an example of the pair redeterminingprocess executed in the observation data error correction section 40that may be executed after the above-described pair determining processshown in FIG. 4 is executed.

In step 600, the pairs of the GPS satellites 10 _(i) used in thepositioning calculation are determined by the above-described pairdetermining process shown in FIG. 4, for example. Once the pairs aredetermined, the processes executed in the sections 42, 44, 46, and 48are executed using the determined pairs as described above. Note that asthe position of the vehicle 20 used in the real solution calculatingsection 44, the positioning result obtained in the above-describedprocess shown in FIG. 5 is preferably used.

In step 602, it is determined whether the integer solution obtainedusing the pairs determined in step 600 is fixed based on the result ofdetermination in the FIX determination section 48. When the integersolution is fixed, it is determined that the pairs determined in step600 are appropriate, and the process ends. On the other hand, when theinteger solution is not fixed, the process proceeds to step 604.

In step 604, pairing is performed in the decreasing order of theabsolute value D_(ik) of the denominator so that the error components Aare small, and the pairs of the GPS satellites 10 _(i) used in thepositioning calculation are redetermined. For example, given that areference satellite is used to secure the linear independence betweenthe observed amounts, the GPS satellite 10 ₁, of which the absolutevalue of D_(ik) is the greatest, may be set as the reference satellite,and four GPS satellites 10 _(i), of which the absolute values of D_(ik)are the next greatest, may be selected and each paired with thereference satellite to determine four pairs. When no reference satelliteis used, four or five GPS satellites 10 _(i), of which the absolutevalues of D_(ik) are the greatest may be selected to determine fourpairs from the selected four or five GPS satellites 10 _(i). In thiscase, similarly to the manner in which the process shown in FIG. 4 isexecuted, four pairs may be determined by pairing two of the selectedfour GPS satellites 10 _(i) that are close to each other in terms ofD_(ik).

According to the process shown in FIG. 6, even when the integer solutionis not fixed in the FIX determination section 48, the pairs of the GPSsatellites 10 _(i) used in the positioning calculation are redeterminedso that the error components Δ are small, and therefore, it is possibleto properly avoid the situation in which the integer solution is notfixed in the FIX determination section 48 and positioning thereforecannot be performed.

In the process shown in FIG. 6, when the pairs of the GPS satellites 10_(i) used in the positioning calculation are redetermined in step 604,the process shown in FIG. 5 may be accordingly executed and the positionof the vehicle 20 may be determined by point positioning with the use ofthe GPS satellites 10 _(i) alone that are included in the redeterminedpairs.

Next, some other examples of the process of determining pairs that isexecuted in the observation data error correction section 40 will bedescribed. Each of the pair determining processes described below may beexecuted instead of the pair determining process shown in FIG. 4 or maybe used in the pair redetermining process (step 604) shown in FIG. 6.

FIG. 7 is a flow chart showing another example of the pair determiningprocess executed in the observation data error correction section 40.

In step 700, A of each of the pairs to be used in the currentpositioning cycle is calculated. The pairs to be used in the currentpositioning cycle may be the same as the pairs used in the precedingpositioning cycle, may be determined by another method, or may berandomly determined.

In step 702, it is determined whether there is A that is calculated inthe above-described step 700, and the absolute value of which is greaterthan a predetermined threshold value β. The predetermined thresholdvalue β corresponds to the error component A such that the integersolution is not fixed in the FIX determination section 48, and thepredetermined threshold value β may be adjusted using the result ofexamination, analysis, etc. When there is Δ, the absolute value of whichis greater than the threshold value β, the process proceeds to step 704.When there is no Δ, the absolute value of which is greater than thethreshold value β, the process proceeds to step 706.

In step 704, it is determined that the pairs to be used in the currentpositioning cycle are not appropriate, and the pairs to be used in thecurrent positioning cycle are changed. In this step, all the pairs maybe changed, or alternatively, only the pair, of which the absolute valueof Δ is greater than the predetermined threshold value β, may bereplaced by another new pair. Such another new pair may be determined bythe method described using FIG. 4, may be determined by another method,or may be randomly determined.

In step 706, it is determined that the pairs to be used in the currentpositioning cycle are appropriate, and the pairs to be used in thecurrent positioning cycle are determined (settled) as the pairs to beused in the current positioning cycle.

According to the process shown in FIG. 7, it is possible to eliminatethe pair, of which the error component Δ exceeds the predeterminedthreshold value β, in the observation data error correction section 40,and therefore, it is possible to realize highly accurate positioning insubsequent sections 44 and 46.

FIG. 8 is a flow chart showing another example of the pair determiningprocess executed in the observation data error correction section 40.

In step 800, Δ is calculated for each of all the possible pairs with theuse of the common GPS satellites 10 _(i) that are being observed by boththe vehicle 20 and the vehicle 30. When the number of the common GPSsatellites 10 _(i) that are being observed by both the vehicle 20 andthe vehicle 30 is N, for example, Δ is calculated for each of the pairs,the number of which is _(N)C₂ (C means combination).

In step 802, a predetermined number of pairs are determined, in theincreasing order of Δ from the pair with the smallest Δ, as the pairsused in the current positioning cycle, based on Δ calculated in theabove-described step 800. The predetermined number is the number ofpairs used in the positioning, which may be a fixed value equal to orgreater than four or may be a variable value equal to or greater thanfour.

According to the process shown in FIG. 8, it is possible to determinethe pairs that give the smallest Δ in the observation data errorcorrection section 40, and therefore it is possible to realize highlyaccurate positioning in subsequent sections 44 and 46.

Note that the process shown in FIG. 8 may be combined with the processshown in FIG. 7, for example. For example, a configuration may beadopted in which in the first positioning cycle, the pairs used in thepositioning are determined by the process shown in FIG. 8, and in thesubsequent positioning cycles, the pairs used in the positioning aredetermined by the process shown in FIG. 7. In this case, the pairs usedin the preceding cycle (the pairs determined by the process shown inFIG. 8) may be determined as the pairs to be used in the currentpositioning cycle in step 700 of the process shown in FIG. 7, and whenthe pairs are changed in step 704, the pairs used in the positioning maybe redetermined by the process shown in FIG. 8.

FIG. 9 is a flow chart showing another example of the pair determiningprocess executed in the observation data error correction section 40.

In step 900, when a particular GPS satellite 10 _(i), among the commonGPS satellites 10 _(i) that are being observed by both the vehicle 20and the vehicle 30, is selected as a reference satellite candidate, Δ iscalculated for each of all the possible pairs, each of which includesthe reference satellite candidate. When the number of the common GPSsatellites 10 _(i) that are being observed by both the vehicle 20 andthe vehicle 30 is N, for example, Δ is calculated for each of the pairs,the number of which is N−1.

In step 902, it is determined whether all the common GPS satellites 10_(i) that are being observed by both the vehicle 20 and the vehicle 30have been selected as the reference satellite candidate. If thedetermination result is positive, the process proceeds to step 906. Ifthe determination result is negative, the process proceeds to step 904.

In step 904, the reference satellite candidate is changed and theprocess returns to step 900. In this way, every one of all the commonGPS satellites 10 _(i) that are being observed by both the vehicle 20and the vehicle 30 is selected as the reference satellite candidate andΔ is calculated for each of all the possible pairs, each of whichincludes the reference satellite candidate.

In step 906, based on the result of calculation in the above-describedstep 900, for each reference satellite candidate, a predetermined numberof pairs are extracted in the increasing order of the absolute value ofΔ from the pair, of which the absolute value of Δ is the smallest, thesum (total value) of the absolute values of Δ of the extracted,predetermined number of pairs is calculated, and the reference satellitecandidate, for which the sum is the smallest, is determined (set) as thereference satellite. The predetermined number is the number of pairsused in the positioning, which may be a fixed value equal to or greaterthan four or may be a variable value equal to or greater than four (notethat the same number is used for all the reference satellitecandidates).

According to the process shown in FIG. 8, it is possible to determinethe pairs that give the smallest Δ in the case where the pairing methodusing a reference satellite is adopted, in the observation data errorcorrection section 40, and therefore it is possible to realize highlyaccurate positioning in subsequent sections 44 and 46. In addition, thepairs that give the smallest Δ are determined in the case where thepairing method using the reference satellite is adopted, so that it ispossible to set the most appropriate reference satellite and realizehighly accurate positioning.

Note that the process shown in FIG. 9 may be combined with the processshown in FIG. 7, for example. For example, a configuration may beadopted in which in the first positioning cycle, the pairs used in thepositioning are determined by the process shown in FIG. 9, and in thesubsequent positioning cycles, the pairs used in the positioning aredetermined by the process shown in FIG. 7. In this case, the pairs usedin the preceding cycle (the pairs determined by the process shown inFIG. 9) may be determined as the pairs to be used in the currentpositioning cycle in step 700 of the process shown in FIG. 7, and whenthe pairs are changed in step 704, the pairs used in the positioning maybe redetermined by the process shown in FIG. 9.

While preferable embodiments of the invention have been described indetail, the invention is not limited to the above-described embodiments,and it is possible to make various modifications and substitutions tothe above-described embodiments without departing from the scope of theinvention.

For example, while in the above-described embodiments, the realsolutions are calculated by the ordinary weighted least square methodusing the weight matrix in which Δ is reflected in the weights, realsolutions may be calculated by the ordinary least square method withoutusing the weight matrix W (that is, the weight matrix W is the identitymatrix). This is because when the pairs that give small Δ as describedabove are determined, the influence of the error component Δ issuppressed and highly accurate positioning result can be expected evenwhen no weight matrix W is used. Conversely, when a weight matrix W isused in which Δ is reflected in the weights, there is no need to use thepair determining method such that Δ become small as described above.Specifically, when a weight matrix W in which Δ is reflected in theweights is used, the pairs that are used in positioning may bedetermined in a random manner (or by a different determining method).Note that also in this case, it is preferable that the pair for which Δbecomes higher than the predetermined threshold value β be changed toanother pair. The weights in the weight matrix W may be determineddepending on another parameter (angle of elevation and/or dilution ofprecision (DOP), for example).

While the above embodiment is a preferable embodiment, in which the realsolutions of the integer ambiguities are calculated by an instantaneouspositioning method, there are various methods of calculating the realsolutions of the integer ambiguities and another method than theabove-described one may be used. For example, a method may be used inwhich the double difference Φ^(jh) _(ku) of the phase accumulation valueis used and the double difference ρ^(jh) _(ku) of the pseudorange is notused. When the GPS receivers 22 and 32 are double frequency receiversthat can receive both the L1 wave and the L2 wave (frequency: 1227.6MHz) emitted from the GPS satellites 10, the double difference Φ^(jh)_(ku) of the phase accumulation value of the L2 wave may be additionallyor substitutionally used as the observed amount Z. Alternatively, thedouble difference Φ^(jh) _(ku) of the phase accumulation value ofanother band carrier wave (radio wave of L5 band that is planned to beadded in the future) may be additionally or substitutionally used as theobserved amount Z. Similarly, also with regard to the double differenceρ^(jh) _(ku) of the pseudorange, the single or double difference ρ^(jh)_(ku) of the pseudorange based on the pseudo random noise (PRN) code,such as P code, other than, but similar to, the C/A code may beadditionally or substitutionally used as the observed amount Z. Whilethe influence of the clock error, the initial phase of the oscillatorsin the GPS receivers 22 and 32, etc. is eliminated by taking the doubledifference as described above in the above-described method ofcalculating the real solutions of the integer ambiguities, aconfiguration may be adopted in which a single difference is taken.While, in the above method, the influence of the ionosphere refraction,the troposphere refraction, and the multipath is ignored, this may betaken into consideration. In another embodiment, a Kalman filter may beused instead of the least square method. In this case, in order not forthe estimation (positioning) result at the preceding epoch to affect theestimation result at the current epoch, instantaneous positioning may beimplemented in which the initialization of the state variables and theerror covariance matrix is performed at every epoch, or a configurationmay be adopted in which the initialization of the state variables andthe error covariance matrix is not performed and the state variables andthe error covariance matrix are updated (passed) at every epoch by usinga normal Kalman filter. In addition, in order to take the kinetic statequantities characteristic of a vehicle due to the movement of thevehicle 30 into consideration, the kinetic state quantities, such as themoving speed of the vehicle, that are obtained using the vehicle sensors(vehicle speed sensor, acceleration sensor, etc.) mounted on the vehicle30 may be input to the Kalman filter as the known input. A mobile bodymodel used to estimate the current state of a vehicle 30 from the travelhistory of the vehicle 30 may be input to the Kalman filter. In thiscase, the mobile body model may be constructed using arbitraryparameters, such as position, speed, acceleration, jerk (derivative ofacceleration), that describe the travel condition of the vehicle 30. Forexample, a mobile body model may be constructed on the assumption thatspeed v of the vehicle 30 is determined by the first-order Markovprocess, and the mobile body model may be input to the Kalman filter.

Part of the various processes executed on the vehicle 20 side in theabove-described embodiment may be executed on the vehicle 30 side, andpart of the various processes executed on the vehicle 30 side in theabove-described embodiment may be executed on the vehicle 20 side. Forexample, the observation data that is observed on the vehicle 30 sidemay be supplied from the vehicle 30 side to the vehicle 20 side and thepositioning process may be executed on the vehicle 20 side. In thiscase, the positioning result is supplied from the vehicle 20 side to thevehicle 30 side through inter-vehicle communication. The positioning(point positioning) of the vehicle 20 may be performed on the vehicle 30side.

While the above-described embodiment concerns the inter-vehicle RTKpositioning between two vehicles 20 and 30, the invention can be used inthe situation where three or more mobile bodies exist. When three ormore mobile bodies exist, similar inter-vehicle RTK positioning may beperformed independently between each pair of the mobile bodies, orinter-vehicle RTK positioning may be performed among the three or moremobile bodies in a cooperative manner. In the latter case, when there isa third vehicle in addition to the vehicles 20 and 30, for example, thevehicle 20 may function as the reference station for both of the vehicle30 and the third vehicle.

While the above-described embodiment concerns the inter-vehicle RTKpositioning between two vehicles 20 and 30, there may be a third mobilebody (vehicle, for example) or a fixed station capable of communicatingwith the vehicles 20 and 30, and the third mobile body or the fixedstation may execute the various processes executed on the vehicle 20side and/or the various processes executed on the vehicle 30 side. Forexample, the third mobile body or the fixed station may acquire theobservation data from both the vehicles 20 and 30 and perform functionsof the sections 40, 42, 44, 46, and 48 on the vehicle 30 side. In thiscase, the positioning result obtained in the third mobile body or thefixed station may be supplied from the third mobile body or the fixedstation to the vehicle 20 and/or the vehicle 30 through radiocommunication.

While the above-described embodiment shows an example in which theinvention is applied to GPS, the invention can be applied to a satellitesystem other than GPS, such as another Global Navigation SatelliteSystem (GNSS), which is Galileo, for example.

1. An inter-mobile body carrier phase positioning device characterized by comprising: first observation data acquisition means that acquires observation data that is observed in a first mobile body and concerns a phase accumulation value of a carrier wave of a satellite signal; second observation data acquisition means that acquires observation data that is observed in a second mobile body and concerns a phase accumulation value of the carrier wave of the satellite signal; satellite pair determination means that determines pairs of satellites used for carrier phase positioning; and carrier phase positioning means that takes, between each of the pairs of the satellites determined by the satellite pair determination means, a single difference or a double difference between the observation data acquired by the first observation data acquisition means and the observation data acquired by the second observation data acquisition means, and determines relative positional relation between the first mobile body and the second mobile body by carrier phase positioning with the use of the single difference or the double difference of the observation data.
 2. The inter-mobile body carrier phase positioning device according to claim 1, wherein: the observation data acquired by the first observation data acquisition means and the observation data acquired by the second observation data acquisition means both include determination data on phase accumulation values of the carrier waves of common satellites and determination data on pseudoranges of the common satellites; and the relative positional relation is determined by an instantaneous positioning method in which the observation data are used independently for each epoch.
 3. The inter-mobile body carrier phase positioning device according to claim 1 or 2, wherein an influence of the single difference or the double difference of the observation data, taken for each of the pairs, on positioning result is regulated by weights, based on a difference between reciprocals of distances between the first mobile body and the pair of the satellites for each of the pairs of the satellites determined by the satellite pair determination means.
 4. The inter-mobile body carrier phase positioning device according to claim 1 or 2, wherein: the carrier phase positioning means determines the relative positional relation with the use of position information of the first mobile body obtained by point positioning along with the single difference or the double difference of the observation data; and the position information of the first mobile body obtained by the point positioning is obtained by the point positioning using only the satellites included in the pairs determined by the satellite pair determination means.
 5. The inter-mobile body carrier phase positioning device according to claim 1 or 2, wherein the satellite pair determination means determines the pairs of the satellites based on the distance between the first mobile body and each of the satellites.
 6. The inter-mobile body carrier phase positioning device according to claim 5, wherein the satellite pair determination means pairs two satellites such that a difference between distances from the first mobile body to the two satellites is relatively small.
 7. The inter-mobile body carrier phase positioning device according to claim 5, wherein the satellite pair determination means pairs two satellites such that a difference between reciprocals of distances from the first mobile body to the two satellites is relatively small.
 8. The inter-mobile body carrier phase positioning device according to claim 5, wherein the satellite pair determination means preferentially selects the satellite, from which a distance to the first mobile body is relatively large, to incorporate into the pairs.
 9. The inter-mobile body carrier phase positioning device according to claim 5, wherein when a difference between reciprocals of distances from the first mobile body to a pair of the satellites exceeds a predetermined threshold value, the satellite pair determination means replaces the pair of the satellites by another pair of the satellites.
 10. The inter-mobile body carrier phase positioning device according to claim 5, wherein when an integer solution derived in the carrier phase positioning means is not fixed, the satellite pair determination means preferentially selects and uses the satellite, from which a distance to the first mobile body is relatively large, to redetermine the pairs.
 11. The inter-mobile body carrier phase positioning device according to any one of claims 1 to 10, wherein: the inter-mobile body carrier phase positioning device is mounted on the second mobile body; the first observation data acquisition means acquires the observation data through radio communication with the first mobile body; and the second observation data acquisition means acquires the observation data through observation of the satellite signal.
 12. An inter-mobile body carrier phase positioning device comprising: a first observation data acquisition section that acquires observation data that is observed in a first mobile body and concerns a phase accumulation value of a carrier wave of a satellite signal; a second observation data acquisition section that acquires observation data that is observed in a second mobile body and concerns a phase accumulation value of the carrier wave of the satellite signal; a satellite pair determination section that determines pairs of satellites used for carrier phase positioning; and a carrier phase positioning section that takes, between each of the pairs of the satellites determined by the satellite pair determination section, a single difference or a double difference between the observation data acquired by the first observation data acquisition section and the observation data acquired by the second observation data acquisition section, and determines relative positional relation between the first mobile body and the second mobile body by carrier phase positioning with the use of the single difference or the double difference of the observation data.
 13. An inter-mobile body carrier phase positioning method characterized by comprising: acquiring first observation data on a satellite signal observed in a first mobile body; acquiring second observation data on a satellite signal observed in a second mobile body; determining pairs of satellites used for carrier phase positioning based on distances from the first mobile body to the satellites so that two of the satellites that are close to each other in terms of the distances are paired; and taking, between each of the determined pairs of the satellites, a single difference or a double difference between the first observation data and the second observation data, and determining relative positional relation between the first mobile body and the second mobile body by carrier phase positioning. 